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1 EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 9-2, 24, pp The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons Herbert J. Sutherland John F. Mandell Sanda Natonal Laboratores Montana State Unversty Albuquerque, NM Bozeman, MT Abstract: In many analyses of wnd turbne blades, the effects of mean stress on the determnaton of damage n composte blades are ether gnored completely or they are characterzed nadequately. Mandell, et al [] have recently presented an updated Goodman dagram for a fberglass materal that s typcal of the materals used n wnd turbne blades. Ther formulaton uses the MSU/DOE Fatgue Data Base [2] to develop a Goodman dagram wth detaled nformaton at thrteen R-values. Usng these data, lnear, b-lnear and full Goodman dagrams are constructed usng mean and 95/95 fts to the data. The varous Goodman dagrams are used to predct the falure stress for coupons tested usng the WISPERX spectrum [3]. Three models are used n the analyses. The frst s the lnear Mner s rule commonly used by the wnd ndustry to predct falure (servce lfetmes). The second s a nonlnear varaton of Mner s rule whch computes a nonlnear Mner s Sum based upon an exponental degradaton parameter. The thrd s a generalzed nonlnear resdual strength model that also reles on an exponental degradaton parameter. The results llustrate that Mner s rule does not predct falure very well. When the mean Goodman dagram s used, the nonlnear models predct falures near the mean of the expermental data, and when the 95/95 Goodman dagram s used, they predct the lower bound of the measured data very well. Keywords: wnd, blades, fatgue, spectral, fberglass. Introducton In many analyses of wnd turbne blades, the effects of mean stress on the determnaton of damage n composte blades are ether gnored completely or they are characterzed nadequately. Mandell, et al [] have recently presented an updated characterzaton of the fatgue propertes for fberglass materals that are * Sanda s a multprogram laboratory operated by Sanda Corporaton, a Lockheed Martn company, for the U.S. Department of Energy under contract DE-AC4-94AL85 typcally used n wnd turbne blades. Ther formulaton uses the MSU/DOE Fatgue Data Base [2] and a three-parameter model to descrbe the mean S-N behavor of the fberglass at thrteen dfferent R- values. The R-value for a fatgue cycle s defned as: mn R = σ σ max, () where σ mn s the mnmum stress and σ max s the maxmum stress n a fatgue stress cycle (tenson s consdered postve and compresson s negatve). The results are typcally presented as a Goodman dagram n whch the cycles-to-falure are plotted as a functon of mean stress and ampltude along lnes of constant R-values. Ths dagram s the most detaled to date, and t ncludes several loadng condtons that have been poorly represented n earler studes. Ths formulaton allows the effects of mean stress on damage calculatons to be evaluated. Usng feld data from the Long term Inflow and Structural Test (LIST) program, Sutherland and Mandell [4] have shown that the updated Goodman dagram predcts longer servce lfetmes and lower equvalent fatgue loads than prevous analyses. Ths predcton s a drect result of the lower damage predcted for the hgh-mean-stress fatgue cycles as a result of usng the updated Goodman dagram. To valdate ths result n a controlled set of experments, the spectral loadng data of Wahl et al [5] s evaluated usng the updated Goodman dagram. These data are from coupons that were tested to falure usng the WISPERX spectrum [3]. Sx formulatons for the S-N behavor of fberglass are used: the frst three use mean fts of the S-N data to construct a lnear, b-lnear and full (3 R-values) Goodman dagram and the second three usng 95/95 fts to construct smlar dagrams (the 95/95 ft mples that, wth a 95 percent level of confdence, the materal wll meet or exceed ths desgn value 95

3 The parameters n these curve fts were selected to provde the best ft to the expermental data and to provde a 9 cycle extrapolaton stress whch was wthn ten () percent of the extrapolaton from a smple two-parameter power law ft to the fatgue data havng lfetmes greater than cycles [] /95 Ft Usng the technques cted n Ref. 8 and 9 and the Standard Practce cted n Ref., the 95/95 curve fts were also determned for these data. The 95/95 ft mples that, wth a 95 percent level of confdence, the materal wll meet or exceed ths desgn value 95 percent of the tme. For these calculatons, we use a one-sded tolerance lmt, whch has been computed and tabulated for several dstrbutons by a number of authors. Typcally, these tabulatons take the followng form: * X X -, X = - c αγ x, (3) where X and X X. are the sample average and the standard devaton, respectvely. The parameter c α,γ s tabulated as a functon of the confdence level ( α), probablty γ and the number of data ponts n. For fatgue fts, the ndependent varable s the stress σ and the dependent varable s the logarthm of the number of cycles to falure N. Thus, the sample average s the log (N) determned from Eq. 2 and the standard devaton X X s gven by: X x n 2 2 ( X - X) = = ( n-) { log N ( σ) - log N ( σ) } = = ( n-) n 2 2. (4) Thus, the number of cycles to falure for the 95/95 ft s gven by: log [ N 95/95] = log [ N ] - log [ N o ], (5) where log [N o ] s tabulated for each of the thrteen R- values n the Table. As shown n Fg., ths technque works well for the fatgue data. However, ths technque does not yeld the 95/95 statc strength that s determned from statc strength data, see the dotted lnes n the fgure. To rectfy ths stuaton, the 95/95 fatgue curve was fared nto the measured 95/95 statc strength, as Table: Parameters for the Thrteen R-Values for Materal DD6 and for Small Strands R-Value Model (Equaton 2) 95/95 (Equaton 5) a b c log (N o ) * *Assumes a frequency of Hz. shown by the sold lnes n the fgure [] s For the analyss of S-N data, the preferred characterzaton s the Goodman dagram. In ths formulaton, the cycles-to-falure are plotted as functons of mean stress and ampltude along lnes of constant R-values. Between R-value lnes, the constant cycles-to-falure plots are typcally, but not always, taken to be straght lnes. Varous Goodman dagrams for the DD-6 fberglass composte are shown n Fgs. 2 and 3. These fgures are presented n ncreasng level of knowledge about the S-N behavor of the fberglass composte materal. Fgures 2a and 3a llustrate the lnear Goodman dagram. In these two fgures, the dagrams are constructed usng the statc strength values for the tensle and compressve ntercepts of the constant lfe curves wth the horzontal axs of the dagram and the S-N data for the R = (see Fg. a) for the ntercepts of the vertcal axs. The b-lnear Goodman dagrams, shown n Fgs. 2b and 3b, are constructed by addng the R =. S-N data (see Fg. b) to the dagram. The full Goodman dagrams, shown n Fgs. 2c and 3c, are constructed by addng the data for the remanng eleven R-values Mean s The Goodman dagrams shown n Fg. 2 were constructed usng Eq. 2 and the nformaton n the Table. Fgures 2a and 2b, use the mean statc strengths for the ntercepts of the constant-lfe curves p. 3

8 Mner's Sum.95 Number of WISPERX Passes: Number of WISPERX Passes: 2 General. General.265 Fg. 8a: Falures Predcted Usng the Mean Full Fg. 9a: Falures Predcted Usng the Mean Full Mner's Sum.95 Number of WISPERX Passes: General. General.265 Number of WISPERX Passes: 2 Fg. 8b: Falures Predcted Usng the 95/95 Full Fg. 8: Comparson of to Predcted Falure usng the Mner s Sum Resdual Strength Models Fg. 9b: Falures Predcted Usng the 95/95 Full Fg. 9: Comparson of to Predcted Falure usng the Generalzed Resdual Strength Models The predctons for Mner s rule usng the three 95/95 Goodman dagrams (see Fg. 3) are shown n Fg. 7b. Agan, the lnear Goodman dagram predcts the longest lfetmes (cycles-to-falure) and the full Goodman dagram predcts the shortest lfetmes. Ths comparson llustrates that the lnear 95/95 Goodman dagram predcts servce lfetmes that are hgher than the measured lfetme, and, the full 95/95 Goodman dagram predcts lfetmes near the mean of the expermental data. Thus, Mner s rule does not predct the measured lfetmes very well. Even the 95/95 Goodman dagrams are non-conservatve n that they predct longer servce lfetmes than those measured n the tests usng the WISPERX load spectrum. At best, the full 95/95 Goodman dagram predcts the mean of measured data. 4.2 Resdual Strength Models The two nonlnear resdual strength models dscussed above were used to predct the lfetmes of the coupons subjected to spectral loadng usng the WISPERX spectrum. The predctons of these models are summarzed n Fgs. 8 and Nonlnear Mner s Sum Model Note the slopes of the predcted lfetme curves shown n Fg. 7 are consstent wth the data, but they are shfted to the rght of the data. The nonlnear Mner s sum model descrbed n Eq. 7 shfts the predcton to the left. Usng a tral-and-error method, a value of =.95 was chosen as the best ft to the experentally measured lfetme data usng the 95/95 Goodman dagram. The predctons for ths resdual strength model are shown n Fg. 8. As shown n ths fgure, the lfetme curves predcted by Mner s rule wth the full Goodman dagrams have been shfted to the left by approxmately a half-decade of cycles. These predctons are n very good agreement wth the measured lfetmes. Namely, the predcted lfetmes are near the mean of the data, see Fg. 8a, when the mean full Goodman dagram s used p. 8

9 Number of WISPERX Passes: 2 Mner's Sum.95 General.265 Fg. a: Falures Predcted Usng the Mean Full Mner's Sum.95 General.265 Number of WISPERX Passes: 2 Normalzed Resdual Strength General.265 General. General.8.2 Number of WISPERX Passes: Cycles to Falure Fg. a: Falures Predcted Usng the Mean Full Normalzed Resdual Strength General.265 General. General.8.2 Number of WISPERX Passes: Cycles to Falure Fg. b: Falures Predcted Usng the 95/95 Full Fg. : Predcted Falure usng the Lnear and the Nonlnear Models Fg. b: Falures Predcted Usng the 95/95 Full Fg. : Resdual Strength usng the Generalzed Nonlnear Model and are at or to-the-left-of the measured lfetmes when the 95/95 full Goodman dagram s used, see Fg. 8b Generalzed Nonlnear Model The predctons for the generalzed nonlnear resdual strength model usng the mean and the 95/95 full Goodman dagrams (see Fg. 3c and 4c) are shown n Fg. 9. As shown n ths fgure, for =, the predcton les essentally on top of the full-goodman Mner s rule predcton. Usng the value chosen by Wahl et al [5] of =.265, the predctons are n general agreement wth the data. Namely, the predcted lfetmes are near the mean of the data when the mean full Goodman dagram s used, see Fg. 9a, and are at or to-the-left-of when the 95/95 full Goodman dagram s used, see Fg. 9b. Thus, the generalzed nonlnear model wth an exponent of.265 s also a good predctor of the measured lfetme when used wth the full Goodman dagram. Note the steps n the predcted lfetme, at approxmately 425 MPa and 5x 3 cycles n Fg. 9a (the begnnng of the plot), and at approxmately 4 MPa and 4 cycles n Fg. 9b. These steps are a drect result of the WISPERX spectrum. As shown n Fg. 6, ths load spectrum contans one very large tenson cycle after approxmately 5 cycles. Ths cycle s the cause of falure at both levels of the cted steps: the predcted falure n Fg. 9a occurs at the frst occurrence of ths relatvely large cycle, and t occurs at the second occurrence n Fg. 9b. For ths falure, the resdual strength s progressvely decreasng, untl t encounters ths relatvely large cycle that exceeds the current resdual strength of the composte. If ths plot had been constructed wth fner resoluton, other, smlar steps would be present Resdual Strength Comparsons Fgures and llustrate the predcted resdual falure strength of the composte usng the lnear Mner s rule and the two nonlnear resdual strength models. p. 9

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